Find the indicated probability. 80% of U.S. drivers over the age of 30 have had a speeding ticket and 55% of tho have also been in an accident while behind the wheel. What is the probability that a randomly selected U.S. driver over the age of 30 ha had a speeding ticket and also been in an accident while behind the wheel? O 0.64 O 0.6875 O 0.3025 O 0.25 O 0.44
Find the indicated probability. 80% of U.S. drivers over the age of 30 have had a speeding ticket and 55% of tho have also been in an accident while behind the wheel. What is the probability that a randomly selected U.S. driver over the age of 30 ha had a speeding ticket and also been in an accident while behind the wheel? O 0.64 O 0.6875 O 0.3025 O 0.25 O 0.44
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
19)
![**Find the indicated probability.**
80% of U.S. drivers over the age of 30 have had a speeding ticket and 55% of those have also been in an accident while behind the wheel.
What is the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel?
- ○ 0.64
- ○ 0.6875
- ○ 0.3025
- ○ 0.25
- ○ 0.44
**Solution Explanation:**
To find the probability, we multiply the probability of each independent event.
Let \( A \) be the event "having a speeding ticket," and \( B \) be the event "been in an accident."
Given,
- \( P(A) = 0.80 \)
- \( P(B|A) = 0.55 \)
We want to find \( P(A \cap B) \), which is \( P(A) \times P(B|A) \).
Calculating:
\[
P(A \cap B) = 0.80 \times 0.55 = 0.44
\]
Thus, the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel is **0.44**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6d8b54a-743c-4fc0-9284-09a62f08bc72%2F0e32afb3-3770-4d25-b88c-2069a50cd311%2Fr0de2yk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the indicated probability.**
80% of U.S. drivers over the age of 30 have had a speeding ticket and 55% of those have also been in an accident while behind the wheel.
What is the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel?
- ○ 0.64
- ○ 0.6875
- ○ 0.3025
- ○ 0.25
- ○ 0.44
**Solution Explanation:**
To find the probability, we multiply the probability of each independent event.
Let \( A \) be the event "having a speeding ticket," and \( B \) be the event "been in an accident."
Given,
- \( P(A) = 0.80 \)
- \( P(B|A) = 0.55 \)
We want to find \( P(A \cap B) \), which is \( P(A) \times P(B|A) \).
Calculating:
\[
P(A \cap B) = 0.80 \times 0.55 = 0.44
\]
Thus, the probability that a randomly selected U.S. driver over the age of 30 has had a speeding ticket and also been in an accident while behind the wheel is **0.44**.
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